Home
Class 12
MATHS
The total number of terms which are depe...

The total number of terms which are dependent on the value of `x` in the expansion of `(x^2-2+1/(x^2))^n` is equal to `2n+1` b. `2n` c. `n` d. `n+1`

A

` 2n+1`

B

2n

C

` n+ 1`

D

n

Text Solution

Verified by Experts

The correct Answer is:
b
Now , ` (x^(2) - 2+ (1)/(x^(2)))^(n) = (x^(4) - 2x^(2) + 1)^(n))/(x^(2n)) = ((x^(2) - 1)^(2n))/(x^(2n))`
` therefore ` Total number of terms that are depandent of x is equal to
number of terms in the expansin of ` (x^(2) -1)^(2n)` that have
degree of x different from 2n , which is given by
` (2n+1) - 1= 2pi` .
Promotional Banner

Topper's Solved these Questions

  • BIONOMIAL THEOREM

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|15 Videos

  • BIONOMIAL THEOREM

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|21 Videos

  • BIONOMIAL THEOREM

    ARIHANT MATHS|Exercise Exercise For Session 4|14 Videos

  • AREA OF BOUNDED REGIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|23 Videos

  • CIRCLE

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|16 Videos

Similar Questions

Explore conceptually related problems

In the expansion of (x^(2) + 1 + (1)/(x^(2)))^(n), n in N ,

The middle term in the expansion of (1 + x)^(2n) is :

Find the (n+1)th term from the end in the expansion of (2x - (1)/(x))^(3n)

If the fourth term in the expansion of (px+1/x)^n is 5/2 , then (n,p)=

The fourth term in the binomial expansion of (x^2-1/x^3)^n is independent of x, when n is equal to:

If the fourth term in the expansion of (a x+1/x)^n is 5/2 , then find the values of a and n.

Write the middle term in the expansion of : (1+x)^(2n) , where n is a positive integer.

If the middle term in the expansion (x^(2)+1//x)^(n) is 924 x^(6) , then find the value of n.

The number of real negative terms in the binomial expansion of (1+i x)^(4n-2),n in N ,x >0 is n b. n+1 c. n-1 d. 2n

The coefficient of x^n , where n is any positive integer, in the expansion of (1+2x+3x^2 +... to oo)^(1//2) is:

ARIHANT MATHS-BIONOMIAL THEOREM-Exercise (Single Option Correct Type Questions)
  1. Solve the following quadratic equation 4x^2 -1 = 0

    Text Solution

    |

  2. The coefficient of x^m in (1+x)^m +(1+m)^(m+1) +...+(1+x)^n ,m≤n is

    Text Solution

    |

  3. The number of values of 'r' satisfying the equation ""^(39)C(3r-1)-...

    Text Solution

    |

  4. The sum S = ""^(20)C(2) + 2*""^(20)C(3) + 3 *""^(20)C(4) + ...+ 19 * "...

    Text Solution

    |

  5. The remainder, if 1+2+2^2++2^(1999) is divided by 5 is.

    Text Solution

    |

  6. The coefficient of 1//x in the expansion of (1+x)^n(1+1//x)^n is (a).(...

    Text Solution

    |

  7. The last two digits of the number 19^(9^(4))is

    Text Solution

    |

  8. If the second term of the expansion [a^(1/(13))+a/(sqrt(a^(-1)))]^n is...

    Text Solution

    |

  9. If 6^(83) + 8^(83) is divided by 49 , the raminder is

    Text Solution

    |

  10. The sum of all rational terms in the expansion of (3^(1//4) + 4^(1...

    Text Solution

    |

  11. Sum of last three digits of the number N=7^(100)-3^(100) is.

    Text Solution

    |

  12. If 5^(99) is divided by 13, the remainder is

    Text Solution

    |

  13. Find the value of {3^(2003)//28}, w h e r e{dot} denotes the fractiona...

    Text Solution

    |

  14. The value of sum(r=0)^(20)r(20-r)(^(20)Cr)^2 is equal to 400^(39)C(20)...

    Text Solution

    |

  15. Find the roots of the following quadratic equation x^2 + x - 1 = 0

    Text Solution

    |

  16. The total number of terms which are dependent on the value of x in the...

    Text Solution

    |

  17. The coefficient of x^(10) in the expansion of (1+x^2-x^3)^8 is 476 b. ...

    Text Solution

    |

  18. The number of real negative terms in the binomial expansion of (1+i x)...

    Text Solution

    |

  19. sum(p=1)^(n) sum(m=p)^(n) (("n"),("m"))(("m"),("p")) is equal to

    Text Solution

    |

  20. The largest real value of x, such that sum(r=0)^(4) ((5^(4-r))/((...

    Text Solution

    |